The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1  1  X  1  1  0  1  1  0  1  1  0  1  1  0  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  X  X  0  1  1  0  1  1  0  1  1  1  1  0  X  X
 0  1  1  0 X+1  1  0 X+1  1  0  1  1  X X+1  1  X X+1  1  X  1  1  X  1  1  0 X+1  1  0 X+1  1  0 X+1  1  0 X+1  1  X  X  X  X  1  1  1  1  1  1  1  1  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0 X+1  1  0 X+1  1  0 X+1  X  1  X  1  1
 0  0  X  0  X  0  X  0  X  X  0  X  X  0  X  0  X  0  X  X  X  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  X  X  X  X  0  0  0  0  0  0  0  X  X  X  0  0  X  X  0  0  X
 0  0  0  X  X  X  X  0  0  0  X  X  0  X  0  X  0  X  X  X  X  0  0  0  0  0  X  X  X  0  X  X  X  0  0  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  X  X  X  X  0  0  X  X  0  0  0  0  0  X  X  X  0  X  X  X  X  X  X  X

generates a code of length 76 over Z2[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+46x^76+15x^80+2x^84

The gray image is a linear code over GF(2) with n=152, k=6 and d=76.
As d=76 is an upper bound for linear (152,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0914 seconds.